The academy graduates are arguably the Blues' two most important players, the pairing contributing 16 goals and 19 assists between them in the Premier League this season.
While it has been claimed that the new Chelsea owners will look to agree fresh terms with the English duo once a takeover is complete, The Times suggests that renewals are not necessarily a foregone conclusion.
The report says that James and Mount want to learn about the club's future plans before they sign extensions at Stamford Bridge.
As it stands, James has three years remaining on his existing deal, while Mount is only tied to the club until the end of 2023-24.
Neither player features among Chelsea's highest earners, something which will need to change if they are to commit their future to the West Londoners.